Lateral buckling of beams - The Behaviour and Design of Steel Structures to EC3 - page 267

beam having the properties of the maximum section of the beam by multiplying
it by

L r
L

1 −

A f , min
A f , max

0.6 + 0.4 d min
d max

α st = 1.0 − 1.2 (6.80)

in which A f , min , A f , max are the flange areas and d min , d max are the section depths
at the minimum and maximum cross-sections, and L r is either the portion of the
beam length which is reduced in section, or is 0.5 L for a tapered beam. This
equation agrees well with the buckling solutions shown in Figure 6.29 for central
concentratedloadsonstepped[59]andtapered[51]beamswhoseminimumcross-
sections are at their simply supported ends.

6.11.2 Design rules

EC3requiresnon-uniformbeamstobedesignedagainstlateralbucklingbyusing
themethodsdescribedinSection6.5.3withthesectionmomentresistance M c , Rd =
W y f y and the elastic buckling moment M cr being the values for the most critical
sectionwheretheratioof M Ed / M c , Rd ofthedesignbendingmomenttothesection
moment capacity is greatest.
Aworked example of checking a stepped beam is given in Section 6.15.7.

L r /L =0

1.0

0.8

Depth tapered
Width tapered
Thickness tapered

L r /L =0.5

0.6

0.4

Mean of width and
thickness stepped

---- r ---- r

2 2

L

0.2

0

0 0.2 0.4 0.6 0.8 1.0

Section parameter (0.6 + 0.4 d min / d max ) A fmin / A fmax

Figure 6.29 Reduction factors for stepped and tapered I-beams.